Radio is the best way to discover new music. With internet radio you can listen to streaming music for free.
A great option is to listen to the Radio Stations in iTunes.

Another great way to discover new music and artists is to open an account in Last.FM and type the kind of music or artist you want to listen. Automatically Last.FM will choose music that you might like according to your preference and you will be able to find new artists you never heard of in the same genre and similar style.
Enjoy new music!: www.last.fm/